A hydrogen atom transitions from #n_i = 1# to #n_f = 7#. What needed to happen to cause this change? Which states did the atom start and end in? What is the change in energy?

1 Answer
Truong-Son N.
Feb 18, 2018

Well, the energy level of any atom is a function of one or more quantum numbers. For hydrogen atom, having only one electron, only #n# matters.

If you transition to a higher #n#, it requires energy, i.e. energy must be supplied.

Clearly, the atom started in state #n = 1#, and ended up in state #n = 7# (it says so in the question).

Therefore, its change in energy, given by the Rydberg equation for hydrogen atom, is

#color(blue)(DeltaE_(1->7)) = -"13.61 eV" cdot (1/n_f^2 - 1/n_i^2)#

#= -"13.61 eV" cdot (1/7^2 - 1/1^2)#

#=# #color(blue)"13.33 eV"#

Does it make physical sense that #DeltaE > 0#? Can you predict what #DeltaE# would be if #n_f = 8# without doing any math, and knowing that it will be within #"0.1 eV"# of what it is with #n_f = 7#?

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